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  • Technical Review
  • Published:

Causal inference for time series

Nature Reviews Earth & Environment volume 4, pages 487–505 (2023)Cite this article

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A Publisher Correction to this article was published on 18 July 2023

This article has been updated

Abstract

Many research questions in Earth and environmental sciences are inherently causal, requiring robust analyses to establish whether and how changes in one variable cause changes in another. Causal inference provides the theoretical foundations to use data and qualitative domain knowledge to quantitatively answer these questions, complementing statistics and machine learning techniques. However, there is still a broad language gap between the methodological and domain science communities. In this Technical Review, we explain the use of causal inference frameworks with a focus on the challenges of time series data. Domain-adapted explanations, method guidance and practical case studies provide an accessible summary of methods for causal discovery and causal effect estimation. Examples from climate and biogeosciences illustrate typical challenges, such as contemporaneous causation, hidden confounding and non-stationarity, and some strategies to address these challenges. Integrating causal thinking into data-driven science will facilitate process understanding and more robust machine learning and statistical models for Earth and environmental sciences, enabling the tackling of many open problems with relevant environmental, economic and societal implications.

Key points

  • Causal inference provides a framework that integrates statistical and machine learning methods to answer causal questions from data.

  • A causal inference analysis enables research questions to be framed as causal questions and transparently lay out the underlying assumptions used to answer these.

  • Causal discovery can be used to learn causal graphs from data to explore and cross-check qualitative causal knowledge.

  • Causal effect estimation allows quantitative causal questions to be answered using a combination of qualitative causal knowledge, statistical or machine learning models and data.

  • Case studies on climate and biogeosciences exemplify the use of causal inference methods and illustrate typical challenges, such as contemporaneous causation, hidden confounding and non-stationarity.

  • Future developments require more interactions between method and domain sciences to better integrate causal thinking into data-driven science.

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Fig. 1: Foundations of causal inference.
Fig. 2: QAD-based causal inference method-selection flow chart.
Fig. 3: Causal inference analysis of the Walker Circulation.
Fig. 4: Non-linear causal effects of temperature on ecosystem respiration.

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Data availability

The original ERA5 reanalysis data for the climate example can be downloaded from https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era5/ or through the KNMI Climate Explorer (https://climexp.knmi.nl) that we also used to extract regional averages.

Code availability

The case studies can be reproduced with Python code provided at https://github.com/jakobrunge/tigramite/blob/master/tutorials/case_studies/, which also includes the data.

The causal inference software packages mentioned in Table 2 are as follows: TETRAD: Java package covering constraint-based, score-based and asymmetry-based causal discovery, as well as causal effect estimation, also for time series, GUI available (https://github.com/cmu-phil/tetrad); causal-learn: Python reimplementation and extension of TETRAD, see above (https://github.com/cmu-phil/causal-learn); pcalg: R package covering constraint-based, score-based and asymmetry-based causal discovery, as well as causal effect estimation (https://CRAN.R-project.org/package=pcalg); Tigramite: Python package covering constraint-based causal discovery and causal effect estimation methods specifically adapted to time series (https://github.com/jakobrunge/tigramite); MXM: R package covering constraint-based causal discovery (https://CRAN.R-project.org/package=MXM); bnlearn/dbnlearn: R package covering constraint and score-based causal discovery (https://CRAN.R-project.org/package=bnlearn), also for time series (https://CRAN.R-project.org/package=dbnlearn); PyWhy: Python package for causal machine learning (https://github.com/py-why); InvariantCausalPrediction: R package covering (sequential) invariant causal prediction (https://cran.r-project.org/package=seqICP); rEDM: R-package for convergent cross mapping (https://cran.r-project.org/web/packages/rEDM/index.html); statsmodels: Python time series modelling package (https://www.statsmodels.org/stable/index.html); Causalnex: Python package for continuous optimization structure learning (https://github.com/quantumblacklabs/causalnex); dagitty: Web-based tool for causal effect estimation via adjustment (http://dagitty.net); CausalFusion: Web-based tool with focus on causal effect estimation and full coverage of do-calculus (https://www.causalfusion.net); Linearmodels: Python modelling package (https://github.com/bashtage/linearmodels); econML: Python package for machine learning-based estimation of causal effects (https://github.com/microsoft/EconML).

Change history

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Acknowledgements

J.R. received funding from the European Research Council (ERC) Starting Grant CausalEarth under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 948112), the European Union’s Horizon 2020 research and innovation programme under grant agreement No 101003469 (XAIDA), the European Union’s Horizon 2020 research and innovation programme under Marie Skłodowska-Curie grant agreement No 860100 (IMIRACLI) and the Helmholtz AI project CausalFlood (grant no. ZT-I-PF-5-11). G.C.-V. and V.E. acknowledge funding from the ERC Synergy Grant USMILE under the European Union’s Horizon 2020 research and innovation programme (grant agreement 855187), and G.C.-V. thanks the Fundación BBVA for support with the project ‘Causal inference in the human-biosphere coupled system (SCALE)’. The authors thank R. Herman, M. Reichstein, E. Bareinboim, E. Galytska and S. Karmouche for helpful comments.

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Authors and Affiliations

  1. Deutsches Zentrum für Luft- und Raumfahrt (DLR), Institut für Datenwissenschaften, Jena, Germany

    Jakob Runge & Andreas Gerhardus

  2. Technische Universität Berlin, Institute of Computer Engineering and Microelectronics, Berlin, Germany

    Jakob Runge

  3. Image Processing Laboratory (IPL), Universitat de València, Paterna, Spain

    Gherardo Varando & Gustau Camps-Valls

  4. Deutsches Zentrum für Luft- und Raumfahrt (DLR), Institut für Physik der Atmosphäre, Weßling, Germany

    Veronika Eyring

  5. University of Bremen, Institute of Environmental Physics (IUP), Bremen, Germany

    Veronika Eyring

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Contributions

J.R. envisaged and drafted the outline of the paper. J.R. and G.C.-V. wrote the Introduction; A.G and G.C.-V. wrote ‘Foundations of causal inference’; J.R. wrote ‘Framing causal research questions’; A.G., J.R. and G.V. wrote ‘Causal discovery’; A.G. wrote ‘Causal effect estimation’; J.R. wrote ‘Example case studies’; and J.R., G.C.-V. and V.E. wrote ‘Recommendations and future perspectives’. All authors discussed the content and contributed to editing the manuscript. All data analyses, Python scripts, Table 1 and all figures were created by J.R.; Table 2 was created by J.R., A.G. and G.V.

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Correspondence to Jakob Runge.

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Runge, J., Gerhardus, A., Varando, G. et al. Causal inference for time series. Nat Rev Earth Environ 4, 487–505 (2023). https://doi.org/10.1038/s43017-023-00431-y

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